Integral representations of the Legendre chi function

Djurdje Cvijović

doi:10.1016/j.jmaa.2006.10.083

paper

Integral representations of the Legendre chi function

arXiv:0911.4731 · doi:10.1016/j.jmaa.2006.10.083

Abstract

We, by making use of elementary arguments, deduce integral representations of the Legendre chi function $χ_{s} (x)$ valid for $∣ z ∣ < 1$ and $ℜ (s) > 1$ . Our earlier established results on the integral representations for the Riemann zeta function $ζ (2 n + 1)$ and the Dirichlet beta function $β (2 n)$ , $n \in N$ , are direct consequence of these representations.

13 pages

Integral representations of the Legendre chi function

Abstract

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